An application of a spectrophotometer using visible light or infrared light is the measurement of the thickness of a thin film or thin layer on a substrate. The principle of the spectroscopic thickness measurement is as follows.
When a ray of incident light (or measurement light) I0 having a single wavelength is cast on a thin layer (or sample) S, as shown in FIG. 8, a part of the light is reflected on the front surface S1 of the sample S, and the remainder enters the sample S. A part of the incoming light is also reflected by the rear surface S2 (i.e. the boundary with the substrate), goes back through the sample S, and goes out through the front surface S1. Since the first reflected light R1 and the second reflected light R2 have different optical path lengths, an interference occurs between the two light waves R1 and R2, depending on the wavelength λ of the measurement light I0 and the thickness d of the sample S. When a graph is drawn with the wavelength (or wavenumber) of the measurement light as the abscissa and the intensity of the interference light as the ordinate while the wavelength of the measurement light is changed (or scanned), a wavy interference spectrum is obtained. The waveform of the interference spectrum can be represented by a cosine function whose cycle interval corresponds to the thickness d of the sample. Therefore, using the interference spectrum, it is possible to determine the thickness d of the sample S by the following steps: automatically or manually measuring the wavenumber at each crest (or peak) or trough (or valley) of the interference spectrum, determining the cycle interval in the wavenumbers between the crests or between the troughs by the least square error method or some other methods, and calculating the thickness d from the wavenumber cycle interval and a known refractive index n.
The interference spectrum obtained through the spectroscopy rarely takes the ideal shape due to various factors, such as the wavenumber dependency of the interference efficiency, the wavenumber dependency of the energy distribution of the light source used, and various noises arising from the apparatus. Conventional methods do not take such factors into account; the methods assume that the waveform of the interference spectrum becomes an ideal cosine curve. Thus, it has been difficult to improve the accuracy of the thickness measurement.
In view of the above problem, the applicant has proposed a method of measuring the thickness of a thin film or thin layer in the Japanese Patent Application No. 2002-147107. For a spectrum obtained by a measurement and represented by a graph with the wavenumber of the incident light as the abscissa and the intensity of the interference light as the ordinate, the method defines an approximate spectrum, called the “constructed spectrum,” by modifying the ideal cosine curve while taking into account various factors that disturb the waveform. The constructed spectrum is represented by a function with thickness d as a variable. Then, a graph is created to show the least square errors between the measured spectrum and the constructed spectrums for various thicknesses, and the thickness corresponding to the minimum point of the least square error is determined as the desired thickness. By taking into account the factors that disturb the waveform of the interference spectrum, the above method has improved the accuracy of the thickness measurement.
In the process of determining the minimum point of the least square error between the constructed spectrum and the measured spectrum by the method of the aforementioned Japanese Patent Application, the thickness d is changed as a parameter to give various waveforms to the constructed spectrum. This method is applicable to the measurement of the thickness of not only a single-layer film but also a multiple layered film.
The measurement of a multiple layered film, however, is possible only when all the layers have the same refractive index n.